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What is the equation of the line that has a slope of 3 and goes through the point [tex]$(-3,-5)$[/tex]?

A. [tex]$y = 3x + 4$[/tex]
B. [tex]$y = 3x - 14$[/tex]
C. [tex]$y = 3x - 4$[/tex]
D. [tex]$y = 3x + 12$[/tex]

Sagot :

GinnyAnswer
To find the equation of a line given a point on the line and the slope, we use the slope-intercept form of the equation of a line, which is:

[tex]\[ y = mx + b \][/tex]

where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

Given:
- The slope [tex]\( m = 3 \)[/tex]
- A point [tex]\( (-3, -5) \)[/tex] that lies on the line

We need to find the y-intercept [tex]\( b \)[/tex]. To do this, we substitute the given point [tex]\( (x, y) \)[/tex] into the equation:

[tex]\[ y = mx + b \][/tex]

Plugging in the values, we get:

[tex]\[ -5 = 3(-3) + b \][/tex]

Now solve for [tex]\( b \)[/tex]:

[tex]\[ -5 = -9 + b \][/tex]

Add 9 to both sides:

[tex]\[ -5 + 9 = b \][/tex]

[tex]\[ b = 4 \][/tex]

So the y-intercept [tex]\( b \)[/tex] is 4. Therefore, the equation of the line is:

[tex]\[ y = 3x + 4 \][/tex]

Thus, the correct answer is:

A. [tex]\( y = 3x + 4 \)[/tex]
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